The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G...The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.展开更多
基金supported by the National Natural Science Foundation of China(No.11871398)the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)+1 种基金the Fundamental Research Funds for the Central Universities(No.3102019ghjd003)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.ZZ2019031)
文摘The degree d(H)of a subgraph H of a graph G is|u∈∪V(H)N(u)-V(H)|,where N(u)denotes the neighbor set of the vertex u of G.In this paper,we prove the following result on the condition of the degrees of subgraphs.Let G be a 2-connected claw-free graph of order n with minimum degreeδ(G)≥3.If for any three non-adjacent subgraphs H1,H2,H3 that are isomorphic to K1,K1,K2,respectively,there is d(H1)+d(H2)+d(H3)≥n+3,then for each pair of vertices u,v∈G that is not a cut set,there exists a Hamilton path between u and v.
